Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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Students are able to… 

  • Apply various strategies, such as make a model, draw a picture, look for a pattern, make a table, etc. to solve problems that provide a context for multiplying fractions with fractions, fractions with whole numbers, and fractions with mixed numbers.
  • Explain how they solved problems using models, pictures, words, and numbers, in their explanation.
  • Work within a group and individually using visual models and determine if their answer makes sense.

Students are able to…because teachers:

  • Provide students with a variety of problems involving equal groups, arrays, and area, that offer opportunities for students to draw pictures or make models.
  • Plan for opportunities during lessons for students to collaborate in small groups to solve problems with visual models and reason through their solution process.

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Questions to ask students:

  • In this problem situation, how did you know to multiply?
    • Sample answer that indicates understanding: In the problem, I know the number of groups and the number in each group so I am looking for the product. This makes it a multiplication problem.
    • Sample answer that indicates an incomplete understanding or a misconception: I am not sure if it is multiplication or division. I think I need to multiply.
  • Why did you draw this type of model when solving this problem?
    • Sample answer that indicates understanding: If I have 3 pieces of ribbon and each piece is 2 ½ inches long, I need to multiply to show 3 groups of 2 ½ inches. My number line model shows the 3 groups of 2 ½ inches.
    • Sample answer that indicates an incomplete understanding or a misconception: I drew a rectangle that is 2 ½ inches long and I divided it into 3 parts.
  • Jayden and Dariel are making a poster for a class assignment. The dimensions of the poster need to be 1 and 1/3  feet by 2 and 1/4   What will be the area of the whole poster?
    • Sample answer that indicates understanding: A student draws the following to show the array made by multiplying the two factors. The student adds all of the partial products in the model for a total of 3 square feet.

 

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FSA Notes

Cognitive Complexity Level: Level 2: Basic Application of Skills & Concepts

Achievement Level Descriptors: (Also assesses 5.NF.2.4)

Level 2: shows the product of a fraction by a whole number using visual fraction models; solves realworld problems involving multiplication of a fraction by a whole number by using visual fraction models or equations to represent the problem

Level 3: finds the product of two fractions by using an area model; generalizes that a/b x c/d = (ac)/(bd) and uses it to solve mathematical or realworld problems involving multiplication of fractions

Level 4: solves real-world problems involving multiplication of fractions and mixed numbers; creates a real-world context involving multiplication of fractions and/or mixed numbers

Level5: finds the possible fractional dimensions of a rectangle given the area; solves multistep mathematical and real-world problems involving multiplication of whole numbers, fractions, and/or mixed numbers

Assessment Limits: MAFS.5.NF.2.6 is assessed with MAFS.5.NF.2.4

  • Visual models may include:
    • Any appropriate fraction model (e.g., circles, tape diagrams, polygons, etc.)
    • Rectangle models tiled with unit squares
  • For tiling, the dimensions of the tile must be unit fractions with the same denominator as the given rectangular shape.
  • Items may not use the terms “simplify” or “lowest terms.”
  • Items may require students to interpret the context to determine operations.
  • Fractions may be greater than 1.
  • For given fractions in items, denominators are limited to 1‐20.

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Additional Resources:

Additional in depth content knowledge:

 

Videos:

Multiply a fraction by a fraction using visual representations

 

Multipy a mixed number by a mixed number using visual representations 

 

Sample Formative Assessment Tasks:

 

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[divider] [/divider]  Resources/Tasks to Support Your Child at Home: